} TAGSAGRA AKADE MIAI LEVELEZO VONATKOZO } AJANL AS A MAGYAR TUDOMANYBAN MEGJELENO A jelolt neve: Pales Zsolt Szuletesi hely, ev, ho, nap: Satoraljaujhely, 1956. marcius 6. Sz}ukebb szakterulete: matematikai analzis, operaciokutatas Doktori ertekezese mely tudomanyteruleten keszult es a vedes eve: matematika, 2001. Tudomanyos es allami kituntetesei (magyar es kulfoldi): Renyi Kato dj (1980), Gr}unwald
Geza Dj (1983), Alexits Gyorgy Dj (1992), 34. ISFE El}oadoi Dj (1996), Marek Kuczma Dj (1998), Bolyai Farkas Dj (2000). Magyar es kulfoldi tudomanyos szervezeti tagsaga, tisztsege: a Bolyai Janos Matematikai Tarsulat, a Magyar Humboldt Tarsasag, az Amerikai Matematikai Tarsasag tagja, a Magyar Operaciokutatasi Tarsasag elnoksegi tagja, az Alkalmazott Matematikai Lapok f}oszerkeszt}oje, a Publicationes Mathematicae Debrecen, a Matematikai Lapok, az Aequationes Mathematicae, a Mathematical Inequalities and Applications, a Journal of Inequalities in Pure and Applied Math ondj Kuratorium ematics folyoiratok szerkeszt}obizottsagi tagja. A Bolyai Janos Kutatasi Oszt szakert}oi kollegiumanak tagja. Jelenlegi munkahelye es beosztasa: Debreceni Egyetem, Analzis Tanszek, egyetemi tanar. Telefon: (52)512-900/2810, Fax: (52)416-857, E-mail:
[email protected]
S INDOKLA Pales Zsolt a matematikai analzis es az operaciokutatas tobb teruleten ert el nemzetkozi visszhangot kivalto eredmenyeket. 123 dolgozata jelent meg, 1 konyvet es 2 konferenciakotetet szerkesztett. Munkaira eddig tobb mint 300 hivatkozast kapott. Megoldotta tobb fontos kozepertek osztalyban az osszehasonltasi, homogenitasi problemat. Megtalalta a kvazielteres kozepek es a sulyfuggvennyel sulyozott kvaziaritmetikai kozepek jellemzeset (Acta Math. Hungar. 40 (1982), 243{260; Aequationes Math. 32 (1987), 171{194) es ezekkel 30 eve nyitott problemakat oldott meg es altalanostotta Kolmogorov, Nagumo es de Finetti 30-as evekbeli eredmenyeit. A linearis ketvaltozos tobb ismeretlen fuggvenyt tartalmazo fuggvenyegyenletekre olyan redukcios eljarast dolgozott ki, amely az ismeretlen fuggvenyekre kozonseges di erencialegyenleteket szolgaltat. Ez az algoritmus lehet}ove teszi ilyen egyenletek megoldasanak szamtogepes meghatarozasat is (Aequationes Math. 43 (1992), 236{247). A fuggvenyiteraciot is tartalmazo fuggvenyegyenletek elmeleteben gyokeresen uj, valos fuggvenytani meggondolasokat alkalmazo modszereket dolgozott ki az ismeretlen fuggvenyek regularitasanak vizsgalatara. Ezekkel a modszerekkel teljes altalanossagban sikerult meghatarozni egy O. Sut^o altal 1914-ben felrt fuggvenyegyenlet megoldasait (Publ. Math. Debrecen 61 (2002), 157-218). A konvexitas stabilitasanak vizsgalataban is alapvet}o eredmenyeket ert el. Sikerult jellemeznie azokat a valos fuggvenyeket, amelyek egy konvex fuggveny korlatos es Lipschitz fuggvennyel valo perturbaciojakent allnak el}o (Proc. Amer. Math. Soc. 131 (2003), 243{252). Debrecen, 2003. augusztus 31. Csaszar Akos az MTA rendes tagja
Daroczy Zoltan az MTA rendes tagja
Katai Imre az MTA rendes tagja
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} TAGSAGRA E NO } AJANL AS AKADE MIAI LEVELEZO TORT Nev: Pales Zsolt Szuletesi hely, ev, ho, nap: Satoraljaujhely, 1956. marcius 6. Anyja neve: Szuchy Maria Tudomanyterulet, ezen belul a sz}ukebb szakterulet: matematika (matematikai analzis, operaciokutatas)
Doktori tudomanyos fokozat, vagy akademiai doktori cm megszerzesenek eve: 2001. Jelenlegi munkahely, beosztas: Debreceni Egyetem, Analzis Tanszek, egyetemi tanar. Telefon: (52)512-900/2810, Fax: (52)416-857, E-mail:
[email protected] Lakcm: 4029 Debrecen, Szappanos u. 21. (nyilvanos)
S INDOKLA Pales Zsolt 1980-ban szerzett matematikus szakon, 1986-ban pedig matematikus-angol szakfordto szakon oklevelet a KLTE-n. 1980-ban a KLTE Analzis Tanszekere kerult, ahol (a bel- es kulfoldi osztondjas id}oszakokat leszamtva) megszaktas nelkul dolgozott. 1982-ben szerzett egyetemi doktori cmet, 1987-ben lett kandidatus, egyetemi docensnek 1988-ban neveztek ki. 1992-93-ban a Saarbruckeni Egyetemen volt Humboldt osztondjas. 1994 es 2001 kozott az Analzis Tanszek vezet}oi, 2001 es 2003 kozott pedig a Debreceni Egyetem Matematikai es Informatikai Intezetenek igazgatoi tisztet latta el. 1997-ben Szechenyi ondjat kapott. MTA doktori ertekezeset 2001-ben vedte meg, egyetemi tanarra 2002-ben Professzori Oszt neveztek ki. Eddigi tudomanyos tevekenyseget 1 konyv es 2 konferenciakotet szerkesztese, 123 megjelent, 11 megjelenes alatt lev}o es 10 kozlesre benyujtott dolgozata, tovabba 2 egyetemi jegyzete alapjan lehet megtelni. Kutatoi tevekenysegenek a jelenlegi intenzitasat mutatja, hogy az elmult ot evben publikalt munkainak szama eleri az 50-et. Dolgozataira eddig tobb mint 300 hivatkozast kapott. Ezek jonev}u folyoiratokban jelentek meg es tobb mint husz tarsszerz}ovel kooperalt. A bemutatott eredmenyek nagy reszet onalloan publikalta, tarsszerz}os dolgozataiban is informacionk van hozzajarulasanak dont}o szereper}ol. Szamos tantvanya van, ezek kozul tobben igen kozel allnak a PhD fokozat eleresehez. Nemzetkozi kapcsolatai szeleskor}uek. Hosszabb id}ot toltott a nemetorszagi Karlsruhei es Saarbruckeni Egyetemeken es a kanadai Waterloo Egyetemen. Tobb alkalommal volt meghvott el}oado es vendegkutato amerikai, kanadai, nemet, osztrak, lengyel es romaniai egyetemeken. Tobb mint 100 alkalommal tartott nemzetkozi konferenciakon, szeminariumokon tudomanyos el}oadast. Ezek mellett idehaza is szvesen vallal es tart a matematikat nepszer}ust}o el}oadasokat. Kezdemenyez}oje es megrendez}oje a Debrecen-Katowice teli szeminarium-sorozatnak. Szamos tovabbi (kb. tz) nemzetkozi konferenciat, szimpoziumot es workshopot szervezett es szervez. Negy nemzetkozi es egy hazai folyoirat szerkeszt}obizottsagi tagja, az Alkalmazott Matematikai Lapok f}oszerkeszt}oje. Megkapta a Renyi Kato, Gr}unwald Geza, Alexits Gyorgy es Bolyai Farkas Djat. 1996-ban elnyerte a 34. ISFE el}oadoi djat. Pales Zsolt a matematikai analzis es az operaciokutatas tobb teruleten ert el nemzetkozi visszhangot kivalto eredmenyeket. Tartalmi szempontbol dolgozatait a kovetkez}okeppen lehet csoportostani: (a) Elteres kozepek es kvaziaritmetikai kozepek elmelete, (b) Hatvanykozepek, Gini es Stolarsky kozepek elmelete, (c) Fuggvenyegyenletek regularitasat javto modszerek, kiterjesztesi tetelek es redukcios eljarasok, (d) Fuggvenyegyenl}otlensegek, fuggvenyegyenletek stabilitaselmelete, (e) Konvexitas altalanostasai, ezek jellemzese, (f) A Hahn-Banach-tetel altalanostasai, (g) Nemlinearis{nemsima analzis es optimalizalas, optimalis iranytaselmelet. Terjedelmi okokbol lehetetlen ezen munkassag reszletes ismertetese, ezert az egyes temakorokb}ol egyket, velemenyunk szerint jellegzetes es fontos eredmenyt probalunk bemutatni. ad (a) A kvaziaritmetikai kozepek 1931-ben Kolmogorov, Nagumo es De Finetti altal egymastol fuggetlenul talalt karakterizacioi motivaltak az altalanosabb kozeposztalyok jellemzesi teteleinek a megkereseset. Ilyen altalanostas pl. a Bajraktarevic altal a 60-as evekben bevezetett un. sulyfuggvennyel
1
sulyozott kvaziaritmetikai kozepek, azaz adott f : I ! R folytonos es szigoruan monoton, valamint p : I ! R pozitv ertek}u fuggveny eseten az alabbi keplettel kepzett p(x )f (x ) + + p(x )f (x ) 1 1 n n Mf;p (x1 ; : : : ; xn ) = f 1 (n 2 N; x1 ; : : : ; xn 2 I ) f (x1 ) + + f (xn ) kozepek. (A p 1 esetben Mf;p egy un. kvaziaritmetikai kozepet szolgaltat.) Ezek jellemzese 30 even at nyitott problema volt. A problemat Pales Zsolt 1987-ben megjelent [18] dolgozataban oldotta meg. n Jellemzesi tetele azt alltja, hogy egy M : [1 uggveny akkor es csak akkor M = Mf;p alaku n=1 I ! I f valamilyen f; p : I ! R fuggvenyekkel, ha re exv, szimmetrikus, kielegt egy bizonyos regularitasi tulajdonsagot, es ha abbol, hogy (x1 ; : : : ; xn ; v1 ; : : : ; vm+k n ) az (u1 ; : : : ; uk ; y1 ; : : : ; ym ) egy permutacioja es teljesulnek az M (x1 ; : : : ; xn ) M (y1 ; : : : ; ym ); M (u1 ; : : : ; uk ) M (v1 ; : : : ; vm+k n ) egyenl}otlensegek mindig kovetkezik, hogy fennall a csatolt M (x1 ; : : : ; xn ; u1 ; : : : ; uk ) M (y1 ; : : : ; ym ; v1 ; : : : ; vm+k n ) egyenl}otlenseg is. Ez az eredmeny, a kvaziaritmetikai kozepek Kolmogorov-fele jellemzeset}ol elter}oen nem fuggvenyegyenletekkel, hanem fuggvenyegyenl}otlensegekkel karakterizalja a sulyfuggvenyel sulyozott kvaziaritmetikai kozepeket. Hasonlo problemat jelentett a Daroczy Zoltan altal 1972-ben bevezetett un. elteres kozepek jellemzese is. Ezt Pales Zsolt 1982-ben talalta meg [2]. Az elteres kozepek osszehasonltasi; komplementer osszehasonltasi; homogenitasi; illetve multiplikativitasi problemait is sikerrel oldotta meg a [1], [10]; [7]; [31]; illetve [6], [13], [25] dolgozatokban. ad (b) Rogztett a; b 2 R, (a b)ab 6= 0 parameterek mellett a (ketvaltozos) Gini, illetve Stolarsky kozepeket az alabbiak szerint szokas ertelmezni: xa + y a 1 b(xa y a ) 1 a b a b Ga;b (x; y) = b b ; Sa;b (x; y) = (x; y > 0; x 6= y); x +y a(xb yb ) tovabba hataratmenettel a fenti ertelmezes az (a b)ab(x y) = 0 esetre is kiterjeszthet}o. Konnyen lathato, hogy mindket kozepertekosztaly magaba foglalja az un. hatvanykozepeket. Pales Zsolt egyik egyszer}uen megfogalmazhato, approximacioelmeleti gondolatokat is felhasznalo tetele a Gini es Stolarsky kozepek osszehasonltasi problemajat oldja meg (vo. [45], [27], [28]). Az emltett eredmeny azt alltja, hogy Ma;b (x; y) Mc;d (x; y) pontosan akkor teljesul minden x; y 2 [ ; ] R+ eseten, ha a + b c + d es Ma;b ( ; ) Mc;d ( ; ), ahol M a G, vagy S kozepek barmelyiket jelentheti. A Gini es Stolarsky kozepekkel kapcsolatos Holder, illetve Minkowski tpusu egyenl}otlensegek lerasa a [8], illetve [3], [64], [72], [92], [126] dolgozatokban tortent meg. ad (c) A fuggvenyegyenletek elmeleteben ismert keves altalanos modszer egyikenek megtalalasa Pales Zsolt nevehez fuz}odik, aki [48] dolgozataban a h1 (x; y)f1 (g1 (x; y)) + + hn (x; y)fn (gn (x; y )) = F (x; y)
((x; y) 2 D R2 )
alaku ketvaltozos fuggvenyegyenletek megoldasara dolgozott ki redukcios eljarast. A modszer alapgondolata olyan fuggvenyegyutthatos parcialis di erencialoperator (algoritmikus) konstrukcioja, amelyet a fenti egyenlet bal es jobb oldalara alkalmazva az f1 ; : : : ; fn ismeretlen fuggvenyek mindegyikere kozonseges differencialegyenlet vezethet}o le. A modszer elegge szamtasigenyes, ezert tantvanyai segtsegevel elkeszult az algoritmus MAPLE implementacioja is. A fuggvenyegyenletek elmeleteben alapvet}o szerepet jatszanak az un. regularitasjavto tetelek, amelyek az egyenletben szerepl}o ismeretlen fuggvenyek gyengebb regularitasat (pl. merhet}oseg, folytonossag, vagy monotonitas) felteve egyszeri, vagy tobbszori di erencialhatosagot alltanak. A fuggvenyiteraciot nem tartalmazo egyenletekre az elmelet Jarai Antal munkassaganak koszonhet}oen teljesedett ki. Pales Zsolt ilyen iranyu eredmenyei els}osorban az olyan fuggvenyosszeteteleket is tartalmazo egyenletekre vonatkoznak, amelyek R. Duncan Luce es Aczel Janos vizsgalatainak koszonhet}oen valtak fontossa (ld. [82], [99], [100], [108], [130]). Az ezekben a dolgozatokban altala kifejlesztett modszer lenyege, hogy el}oszor a fuggvenyegyenlet felhasznalasaval az un. bels}o fuggvenyekre fuggvenyegyenl}otlenseget (pl. Jensen-konvexitast) vezet le, majd alkalmazza a fuggvenyegyenl}otlensegek regularitas elmeletet (pl. Bernstein-Doetsch-tetel), es gy nyeri a bels}o fuggveny er}osebb regularitasi tulajdonsagait. Ezeknek a modszereknek az alkalmazasaval sikerult [117]-ben megoldani (extra regularitasi feltevesekt}ol mentesen) az 1914-ben Sut^o altal felvetett f (x) + f (y ) g (x) + g (y ) f 1 +g 1 =x+y (x; y 2 I ) 2 2
2
egyenletet, ahol f; g : I ! R szigoruan monoton es folytonos fuggvenyek. A megoldas alapvet}o lepeseiben el}oszor (a valos fuggvenytan tobb nom eredmenyet es meggondolasat is alkalmazva) azt kell igazolni, hogy f; f 1 ; g; g 1 lokalisan Lipschitz, majd di erencialhato, vegul, hogy folytonosan di erencialhato. A fenti egyenlettel, illetve altalanostasaival kapcsolatos tovabbi vizsgalatok talalhatok a [94], [98], [104], [113], [125], [128], [132], [137], [138] dolgozatokban. ad (d) A konvexitas stabilitasi kerdesei vezettek el a f (tx + (1 t)y) tf (x) + (1 t)f (y) + + "t(1 t)jx yj
(x; y 2 I; t 2 [0; 1])
fuggvenyegyenl}otlenseg vizsgalatahoz (ahol ; " nem negatv konstansok). Pales Zsolt meglep}o eredmenye (ld. [122]) szerint egy f : I ! R fuggveny akkor es csak akkor tesz eleget a fenti egyenl}otlensegnek, ha el}oall egy konvex, egy korlatos es egy Lipschitz fuggveny osszegekent. Az un. Wright es a Jensen-konvexitas stabilitasaval kapcsolatos legujabb eredmenyeket a [109] es [133] dolgozatokban erte el. A fuggvenyegyenletek stabilitaselmeleteben az un. direkt modszerrel es az un. invarians kozep technikaval egyarant fontos eredmenyeket ert el (ld. [56], [77], [85], [96], [102], [105], [124]). A Tabor altal bevezetett kvaziadditv fuggvenyekr}ol [75]-ben bebizonytotta, hogy ezek pontosan az egy Lipschitz es egy additv fuggveny kompoziciojakent el}oallo fuggvenyek. Kazimierz Nikodemmel kozos [73] dolgozataban a szigoruan monoton es folytonos valamint additiv fuggvenyek kompoziciojakent el}oallo fuggvenyeket jellemezte. Ezert a dolgozatert a lengyelorszagi Marek Kuczma verseny els}o djat kapta 1998-ban. ad (e) A Jensen-konvex fuggvenyek elmeleteben alapvet}o Bernstein-Doetsch-fele regularitasi tetel kiterjesztese talalhato a [95]-ben. A konvexitas kulonboz}o (fuggvenyegyutthatos, magasabbrend}u) altalanostasait es ezek jellemzeseit vizsgaljak meg a [23], [44], [90], [93], [118], [127], [129], [131], [136] dolgozatok. ad (f) A Hahn-Banach-tetel egyik valtozata szerint egy linearis terben diszjunkt kupok (bizonyos topologiai mellekfeltetelek teljesulese eseten) linearis funkcionalokkal elvalaszthatok. Ennek az eredmenynek a kommutatv felcsoportokra torten}o altalanostasait dolgozta ki Pales Zsolt [33], [34]-ben. Megmutatta, hogy egy kommutatv felcsoport diszjunkt reszfelcsoportjai (bizonyos topologiai mellekfeltetelek teljesulese eseten) additv fuggvenyekkel szeparalhatok. Ennek a tetelnek erdekes alkalmazasait talalta az elteres kozepek elmeleteben es a dontesfuggvenyek karakterizacioiban ([32], [19]). A [103] dolgozatban a Hahn-Banach, illetve a Dubovickij{Miljutyin-fele szeparacios tetelek transzfomaciocsoportokra nezve invarians elvalsztasi teteleit talalta meg. ad (g) Az erint}osokasagok Ljuszternyikt}ol szarmazo lerasa alapvet}oen fontos a Banach-terbeli szels}oertekproblemak vizsgalataban. [69] dolgozataban ezt a tetelt altalanostotta a di erencialhatosagi feltetelek lenyeges gyengtesevel, ezzel lehet}ove teve a nemsima egyenl}osegi korlatozasokat tartalmazo szels}oertekproblemak vizsgalatat ([54]). Az optimalis iranytaselmelet kulonboz}o nemsima allapotter es iranytasi korlatozasokat tartalmazo feladataiban az un. Dubovickij{Miljutyin modszer alkalmazasaval sikerult a Pontrjagin-fele maximumelv igazolasa es tovabbi masodrend}u szukseges feltetelek levezetese ([54], [57], [58], [61], [76], [97], [106], [121], [134], [135], [139]). A masodrend}u feltetelek (nemsima adatok melletti) megfogalmazasat tette lehet}ove a [63] dolgozatban bevezetett masodrend}u derivalt fogalom. A fentiek alapjan osszefoglaloan megallapthato, hogy Pales Zsolt tudomanyos munkassagara a szeleskor}u erdekl}odes, egy-egy teruleten valo elmelyules es az alkalmazasokra valo erzekenyseg jellemz}o. Kutatoi, oktatoi, tudomanyszervez}oi tevekenysegevel nagy mertekben hozzajarult a debreceni analzis, es ezen belul a fuggvenyegyenletek es egyenl}otlensegek iskola hrnevenek oregbtesehez, tudomanyos kapcsolatainak a kiszelestesehez. Mindezek alapjan javasoljuk, hogy Pales Zsoltot a Magyar Tudomanyos Akademia valassza tagjai soraba. Debrecen, 2003. augusztus 31. Csaszar Akos az MTA rendes tagja
Daroczy Zoltan az MTA rendes tagja
Katai Imre az MTA rendes tagja
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Prekopa Andras az MTA rendes tagja
Pales Zsolt tudomanyos kozlemenyei Referalt folyoiratokban es konferenciakiadvanyokban megjelent dolgozatok es disszertaciok (hivatkozasi adatokkal kiegesztve) [1] Z. Daroczy | Zs. Pales, On comparison of mean values, Publ. Math. Debrecen 29 (1982), 107-116. [MR: 84e #39007], [ZBl: 508.26010] Hivatkozasok: H1. J. Aczel | J. G. Dhombres, Functional equations in several variables, Cambridge University Press, New York-New Rochelle-Melbourne-Sidney, 1989. H2. P. S. Bullen | D. S. Mitrinovic | P. M. Vasic, Means and Their Inequalities, D. Reidel Publ. Co., Dordrecht, 1988. H3. E. Castillo Ron | M. R. Ruiz-Cobo, Functional Equations and modelling in Science and Ingineering, Pure and Applied Mathematics, Marcel Dekker Inc., New York-Basel-Hong Kong, 1992. H4. E. Castillo Ron | M. R. Ruiz-Cobo, Ecuaciones funcionales y modelizacion en Ciencia, Ingeniera y Economa, Edittorial Reverte, S. A., Barcelona-Bogota-Buenos Aires-Caracas-Mexico, 1993. H5. J. G. Dhombres, Some recent applications of functional equations, in: History, Applications and Theory of Functional Equations (ed. by J. Aczel), D. Reidel Publ. Co., Dordrecht, 1984, 67-91. H6. D. S. Mitrinovic | J. E. Pecaric, Srednje, vrednosti u matematici, Naucna Knjiga, Beograd, 1989. H7. P. Muliere | G. Parmigiani, Utility and means in the 1930s, Stat. Sci. 8 (1993), 421-422.
[2] Zs. Pales, Characterization of quasideviation means, Acta Math. Hungar. 40 (1982), 243-260. [MR: 84j #26018], [ZBl: 541.26006] Hivatkozasok: H8. J. Aczel | J. G. Dhombres, Functional equations in several variables, Cambridge University Press, New York-New Rochelle-Melbourne-Sidney, 1989. H9. L. R. Berrone, Decreasing sequences of means appearing from non-decreasing functions, Publ. Math. Debrecen 55 (1999), 53-72. H10. P. S. Bullen | D. S. Mitrinovic | P. M. Vasic, Means and Their Inequalities, D. Reidel Publ. Co., Dordrecht, 1988. H11. E. Castillo Ron | M. R. Ruiz-Cobo, Functional Equations and modelling in Science and Ingineering, Pure and Applied Mathematics, Marcel Dekker Inc., New York-Basel-Hong Kong, 1992. H12. E. Castillo Ron | M. R. Ruiz-Cobo, Ecuaciones funcionales y modelizacion en Ciencia, Ingeniera y Economa, Edittorial Reverte, S. A., Barcelona-Bogota-Buenos Aires-Caracas-Mexico, 1993. H13. L. Losonczi, Holder-type inequalities, General Inequalities 3, (Oberwolfach, 1981), (ed. E. F. Beckenbach and W. Walter), Birkhauser Verlag, Basel-Boston-Stuttgart, 1983, 107-122. H14. D. S. Mitrinovic | J. E. Pecaric, Srednje, vrednosti u matematici, Naucna Knjiga, Beograd, 1989. H15. P. Muliere | G. Parmigiani, Utility and means in the 1930s, Stat. Sci. 8 (1993), 421-422.
[3] Zs. Pales, A generalization of the Minkowski inequality, J. Math. Anal. Appl. 90 (1982), 456-462. [MR: 84j #26024], [ZBl: 504.26008] Hivatkozasok: H16. L. Losonczi, Restricted subadditivity of homogeneous means, J. Math. Anal. Appl. 222 (1998), 167-176. H17. D. S. Mitrinovic | J. E. Pecaric, Srednje, vrednosti u matematici, Naucna Knjiga, Beograd, 1989. H18. D. S. Mitrinovic | J. E. Pecaric | A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Acad. Publ., Dordrecht, 1993. H19. B. Mond | J. E. Pecaric, Generalized power means for matrix functions, Publ. Math. Debrecen 46 (1994), 33-41. H20. B. Mond | J. E. Pecaric, Generalized power means for matrix functions II, Publ. Math. Debrecen 48 (1996), 201-208. H21. J. E. Pecaric, Konveksne Funkcije { Nejednakosti, Naucna Knjiga, Beograd, 1987. H22. J. E. Pecaric | F. Proschan | Y. L. Tong, Convex functions, partial orderings, statistical applications, Math. Sci. Eng. 187, Academic Press, Boston, 1992.
[4] Zs. Pales, Kvazielteres{kozepertekek es egyenl}otlensegek, egyetemi doktori ertekezes, KLTE Debrecen, 1982. [5] Zs. Pales, Inequalities for homogeneous means depending on two parameters, General Inequalities 3, (Oberwolfach, 1981), (ed. E. F. Beckenbach and W. Walter), Birkhauser Verlag, Basel-BostonStuttgart, 1983, 107-122. [MR: 86i #26018], [ZBl: 572.26010] Hivatkozasok: H23. P. S. Bullen | D. S. Mitrinovic | P. M. Vasic, Means and Their Inequalities, D. Reidel Publ. Co., Dordrecht, 1988. H24. D. S. Mitrinovic | J. E. Pecaric, Srednje, vrednosti u matematici, Naucna Knjiga, Beograd, 1989.
[6] Z. Daroczy | Zs. Pales, Multiplicative mean values and entropies, Colloquia Math. Soc. J. Bolyai 35., Functions, Series, Operators, (Budapest, 1980), North Holland, Amsterdam-New York, 1983, 343-359. [MR: 86c #39008], [ZBl: 558.94002] Hivatkozasok:
1
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[52] Zs. Pales, Inverse function theorems for nonsmooth mappings in Banach spaces, in: Operation Research '93, (Koln, 1993), (ed. by A. Bachem | U. Derigs | M. Junge | R. Schrader), Physica Verlag, 1994, 385-388. [53] Zs. Pales, Linear selections for set-valued functions and extension of bilinear forms, Arch. Math. (Basel) 62 (1994), 427-432. [MR: 95h #46009], [ZBl: 797.46005] Hivatkozas: H186. R. Badora, On the separation with n-additive functions, General Inequalities 7, (Oberwolfach, 1995), (ed. C. Bandle), Birkhauser Verlag, Basel-Boston-Stuttgart, 1997, 119-230.
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H195. U. Ledzewicz | H. Schattler, High order tangent cones and their application in optimization, Nonlinear Anal., Theory, Methods, Appl. 30 (1997), 2449-2460. H196. U. Ledzewicz | H. Schattler, High order approximations and generalized necessary conditions for optimality, SIAM J. Control Optim. 37 (1999), 33-53. H197. U. Ledzewicz | H. Schattler, A Higher-order generalized maximum principle, SIAM J. Control Optim. 38 (2000), 823-854. H198. U. Ledzewicz | H. Schattler, On generalizations of the Euler-Lagrange equation, Nonlinear Anal., Theory, Methods, Appl. 47 (2001), 339-350. H199. J.-P. Penot, Second-order conditions for optimization problems with constraints, SIAM J. Control Optim. 37 (1999), 303-318. H200. J.-P. Penot, Recent advances on second-order optimality conditions, Optimization 481 (2000), 357-380. H201. M. Studniarski, Higher-order necessary optimality conditions in terms of Neustadt derivatives, Nonlinear Anal., Theory, Methods, Appl. 47 (2001), 363-373. H202. V. Zeidan, Admissible directions and generalized coupled points for optimal control problems, Nonlinear Anal., Theory, Methods, Appl. 26 (1996), 479-507.
[55] Zs. Pales, General necessary and sucient conditions for constrained optimum problems, Arch. Math. (Basel) 63 (1994), 238-250. [MR: 95f #49032], [ZBl: 808.49026] [56] Zs. Pales, Bounded solutions and stability of functional equations for two variable functions, Resultate der Math. 26 (1994), 360-365. [MR: 96a #39034], [ZBl: 834.39012] Hivatkozasok: H203. B. Ebanks, Bounded solutions of n-cocycle and related equations on amenable semigroups, Result. Math. 35 (1999), 23-31. H204. L. Szekelyhidi, Ulam's problem, Hyers's solution | and to where they led, Functional Equations and Inequalities, (ed. Th. M. Rassias), Mathematics and Its Applications, Vol. 518, Kluwer Acad. Publ., Dordrecht{Boston{London, 2000, pp. 259-285.
[57] Zs. Pales | V. Zeidan, First and second order necessary conditions for control problems with constraints, Trans. Amer. Math. Soc. 346 (1994), 421-455. [MR: 95b #49034], [ZBl: 819.49017] Hivatkozasok: H205. J. F. Bonnans | H. Zidani, Optimal control problems with partially polyhedric constraints, SIAM J. Control Optim. 37 (1999), 1726-1741. H206. H. Kawasaki | S. Koga, Legendre conditions for variational problem with one-sided phase constraints, J. Oper. Res. 38 (1995), 483-492. H207. S. Koga | H. Kawasaki, Legendre-type optimality conditions for a variational problem with inequality state constraints, Math. Program. 84 (1999), 421-434. H208. H. Kawasaki | V. Zeidan, Conjugate points for variational problems with equality and inequality state constraints, SIAM J. Control Optim. 39 (2000), 433-456. H209. U. Ledzewicz | H. Schattler, An extended maximum principle, Nonlinear Anal., Theory, Methods, Appl. 29 (1997), 159-183. H210. U. Ledzewicz | H. Schattler, A second-order Dubovitskii-Milyutin theory and applications to control, In: Sivasundaram, S. (ed.) Advances in Nonlinear Dynamics, Stability Control Theory Methods Appl. 5, Gordon and Breach, Amsterdam, 1997, 179-192. H211. U. Ledzewicz | H. Schattler, High order tangent cones and their application in optimization, Nonlinear Anal., Theory, Methods, Appl. 30 (1997), 2449-2460. H212. U. Ledzewicz | H. Schattler, High order approximations and generalized necessary conditions for optimality, SIAM J. Control Optim. 37 (1999), 33-53. H213. U. Ledzewicz | H. Schattler, A Higher-order generalized maximum principle, SIAM J. Control Optim. 38 (2000), 823-854. H214. U. Ledzewicz | H. Schattler, On generalizations of the Euler-Lagrange equation, Nonlinear Anal., Theory, Methods, Appl. 47 (2001), 339-350. H215. J.-P. Penot, Recent advances on second-order optimality conditions, Optimization 481 (2000), 357-380. H216. M. D. R. de Pinho, Maximum principle for mixed constrained control problem, Nonlinear Anal., Theory, Methods, Appl. 47 (2001), 387-398. H217. M. D. R. de Pinho | A. Ilchmann, Weak maximum principle for optimal control problems with mixed constraints, Nonlinear Anal., Theory, Methods, Appl. 48(8) (2002), 1179-1196. H218. V. Zeidan, Admissible directions and generalized coupled points for optimal control problems, Nonlinear Anal., Theory, Methods, Appl. 26 (1996), 479-507.
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[59] Zs. Pales, Separation with symmetric bilinear forms and symmetric selections of set-valued functions, Publ. Math. Debrecen 46 (1995), 321-331. [MR: 96g #46003], [ZBl: 860.46002] , Hivatkozasok: H219. R. Badora, On the separation with n-additive functions, General Inequalities 7, (Oberwolfach, 1995), (ed. C. Bandle), Birkhauser Verlag, Basel-Boston-Stuttgart, 1997, 119-230. H220. A. Eberhard, Prox-regularity and subjets, Optimization and related topics (Ballarat, Australia, 1999), (eds. A. Rubinov | B. Glover), Kluwer Acad. Publ., Dordrecht, Appl. Optim. Vol. 47, 2001, pp. 237-313.
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[64] L. Losonczi | Zs. Pales, Minkowski's inequality for two variable Gini means, Acta Sci. Math. (Szeged) 62 (1996), 413-425. [MR: 98c #26012], [ZBl: 880.26010] Hivatkozasok: H232. H. Alzer | S. Ruscheweyh, On the intersection of two-parameter mean value families, Proc. Amer. Math. Soc. 129 (2001), 2655-2662. H233. L. Losonczi, Equality of two variable quasiarithmetic mean values weighted with a weightfunction, Aequationes Math. 58 (1999), 223-241.
[65] D. Gronau | Zs. Pales (Editors), Contributions to the theory of functional equations II, 2nd Proceedings of the Seminar Debrecen-Graz, Zamardi, May 11-14, 1995. Grazer Math. Ber. 327 (1996). [MR: 98d #39001], [ZBl: 881.00032] [66] Zs. Pales, Notes on mean value theorems, in Contributions to the Theory of Functional Equations II (eds. D. Gronau and Zs. Pales), Grazer Math. Ber. 327 (1996), 17-20. [MR: 98i #26006], [ZBl: 905.26004] [67] L. Losonczi | Zs. Pales, Inequalities for inde nite forms, J. Math. Anal. Appl. 205 (1997), 148-156. [MR: 98e #26021], [ZBl: 871.26012] Hivatkozasok: H234. F. Saidi, Generalized inequalities for inde nite forms, J. Pure Appl. Math. kozlesre elfogadva. H235. F. Saidi | R. Younis, Generalized Holder-like inequalities, Rocky Mountain J. Math. 29 (1999), 14911503.
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[68] Zs. Pales, Separation by semide nite bilinear forms, General Inequalities 7, (Oberwolfach, 1995), (ed. C. Bandle), Internat. Ser. Numer. Math. 123, Birkhauser Verlag, Basel-Boston-Stuttgart, 1997, pp. 259-267. [MR: 98g #46004], [ZBl: 916.46003] [69] Zs. Pales, Inverse and implicit function theorems for nonsmooth maps in Banach spaces, J. Math. Anal. Appl. 209 (1997), 202-220. [MR: 98b #49018], [ZBl: 880.58002] Hivatkozasok: H236. J. M. Borwein | A. L. Dontchev, On the Bartle-Graves theorem, Proc. Amer. Math. Soc. 131 (2003), 2553-2560. H237. A. Domokos, A note on an inverse function theorem by D. Aze, Mathematica (Cluj) 40(63) (1998), 79-83. H238. B. Slezak, A right inverse function theorem without assuming di erentiability, Studia Sci. Math. Hung. 36 (2000), 153-164.
[70] S. S. Dragomir | B. Mond | Zs. Pales, On a superadditivity property of Gram's determinant, Aequationes Math. 54 (1997), 199-204. [MR: 98j #46018], [ZBl: 890.26015] Hivatkozas: H239. S. S. Dragomir | B. Mond, On a property of Gram's determinant, Extracta Math. 11 (1996), 282-287. [71] Zs. Pales | V. Zeidan, On the representation of certain bilinear forms on C (T ) and L1 (T ), Acta Sci. Math. (Szeged) 63 (1997), 497-511. [MR: 99g #49016], [ZBl: 893.46017] [72] L. Losonczi | Zs. Pales, Minkowski's inequality for two variable di erence means, Proc. Amer. Math. Soc. 126 (1998), 779-791. [MR: 98e #26022], [ZBl: 908.26016] Hivatkozasok: H240. H. Alzer | S. Ruscheweyh, On the intersection of two-parameter mean value families, Proc. Amer. Math. Soc. 129 (2001), 2655-2662. H241. L. Losonczi, Homogeneous Cauchy mean values, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 209-218. H242. L. Losonczi, Inequalities for Cauchy mean values, Math. Inequal. Appl. 5 (2002), 349-359. H243. L. Losonczi, Equality of two variable Cauchy mean values, Aequationes Math. 65 (2003), 61-81. H244. J. Matkowski | J. Ratz, Convex functions with respect to an arbitrary mean, General Inequalities 7, (Oberwolfach, 1995), (ed. C. Bandle), Birkhauser Verlag, Basel-Boston-Stuttgart, 1997, 249-258.
[73] K. Nikodem | Zs. Pales, A characterization of midpoint-quasiane functions, Publ. Math. Debrecen 52 (1998), 575-595. [MR: 99g #39034], [ZBl: 910.39006] Hivatkozas: H245. Z. Boros, Strongly Q-di erentiable functions, Real Anal. Exchange 27 (2002). [74] Zs. Pales, First and higher order necessary conditions for optimization problems via a DubovitskiiMilytin type approach, Proc. of the 1998 Baikal International Summer School on Optimization, Optimization Methods and their Applications (ed. V. P. Bulatov), Institute of Energy Systems, Irkutsk, 1998, 193-204. [75] Zs. Pales, Generalized stability of the Cauchy functional equation, Aequationes Math. 56 (1998), 222-232. [MR: 99k #39076], [ZBl: 922.39008] Hivatkozasok: H246. A. Gilanyi, Hyers-Ulam stability of monomial functional equations on a general domain, Proc. Natl. Acad. Sci. USA, 96 (1999), 10588-10590. H247. G. H. Kim, The stability of functional equations with a square-symmetric operation, Math. Inequal. Appl. 4 (2001), 257-266. H248. J. Tabor, Monomial selections of set-valued functions, Publ. Math. Debrecen, 56 (2000), 33-42. H249. J. Tabor, Hyers theorem and the cocycle property, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 275-290.
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[77] Zs. Pales | P. Volkmann | D. Luce, Stability of functional equations with square-symmetric operations, Proc. Natl. Acad. Sci. U.S.A. 95 (1998), 12772-12775. [MR: 2000a #39030], [ZBl: 930.39020] Hivatkozasok: H251. K. Baron | P. Volkmann, On functions close to homomorphisms between square symmetric structures, http://www.mathematik.uni-karlsruhe.de/semlv, Seminar LV, 14 (2002), 12 pp. H252. A. Gilanyi, Hyers-Ulam stability of monomial functional equations on a general domain, Proc. Natl. Acad. Sci. USA, 96 (1999), 10588-10590. H253. G. H. Kim, The stability of functional equations with a square-symmetric operation, Math. Inequal. Appl. 4 (2001), 257-266. H254. G. H. Kim | Y. W. Lee | K. S. Ji, Modi ed Hyers{Ulam{Rassias stability of functional equations with square-symmetric operation, Commun. Korean Math. Soc. 16 (2001), 211-223.
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[78] Zs. Pales, Geometric versions of Rode's theorem, Radovi Matematicki 8 (1992/1998), 1-13. [MR: 2000g #46004], [ZBl: 937.46005] Hivatkozasok: H255. P. W. Cholewa, A geometric view on -convex functions, Grazer Math. Ber. 316 (1992), 29-36. H256. D. H. Hyers | G. Isac | Th. M. Rassias, Stability of functional equations in several variables, (Progress in Nonlinear Di erential Equations and their Applications 34, Birkhauser Verlag, 1998.
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[81] G. Kassay | J. Kolumban | Zs. Pales, On Nash stationary points, Publ. Math. Debrecen 54 (1999), 267-279. [MR: 2000c #90074], [ZBl: 932.49009] Hivatkozas: H258. G. Kassay | J. Kolumban, System of multi-valued variational inequalities, Publ. Math. Debrecen 56 (2000), 185-195.
[82] J. Aczel | Gy. Maksa | Zs. Pales, Solutions to a functional equation arising from di erent ways of measuring utility, J. Math. Anal. Appl. 233 (1999), 740-748. [MR: 2000f #39026], Hivatkozasok: H259. J. Aczel | J-C. Falmagne | R. D. Luce, Functional equations in the behavioral sciences, Math. Japonica, 52(3) (2000), 469-512. H260. J. Aczel | R. D. Luce | C. T. Ng, Functional equations arising in a theory of non-commutative joint receipt, kozlesre benyujtva. H261. R. D. Luce, Personal re ections on an unintentional behavioral scientist, Aequationes Math. 58 (1999), 3-15. H262. R. D. Luce, Utility of gains and losses: Measurement-theoretical and Experimental Approaches, Scienti c Psychology Series, Lawrence Erlbaum Associates, Publishers, Mahwah{New Jersey{London, 2000. H263. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[83] Zs. Pales | V. Zeidan, On L1 -closed decomposable sets in L1 in Systems modelling and optimization (Detroit, MI, 1997), Chapman & Hall/CRC, Boca Raton, FL, 1999, pp. 198-206, [MR: 2000a #46047], [ZBl: 955.46017] [84] Zs. Pales | V. Zeidan, Characterization of closed and open C -convex sets in C (T; Rr ), Acta Sci. Math. (Szeged) 65 (1999), 339-357. [MR: 2000g #49021], [ZBl: 932.54018] [85] R. Badora | Zs. Pales | L. Szekelyhidi, Monomial selection of set-valued maps, Aequationes Math. 58 (1999), 214-222. [MR: 2001a #39062], [ZBl: 964.39020] Hivatkozasok: H264. A. Gilanyi, Hyers-Ulam stability of monomial functional equations on a general domain, Proc. Natl. Acad. Sci. USA, 96 (1999), 10588-10590. H265. A. Gilanyi, Local stability and global superstability of monomial functional equations, Advances in Equations and Inequalities (ed. J. M. Rassias), Hadronic Press, Palm Harbor, 1999, 73-95. H266. L. Szekelyhidi, Ulam's problem, Hyers's solution | and to where they led, Functional Equations and Inequalities, (ed. Th. M. Rassias), Mathematics and Its Applications, Vol. 518, Kluwer Acad. Publ., Dordrecht{Boston{London, 2000, pp. 259-285. H267. J. Tabor, Monomial selections of set-valued functions, Publ. Math. Debrecen, 56 (2000), 33-42.
[86] Zs. Pales | V. Zeidan, Characterization of L1 -closed decomposable sets in L1 , J. Math. Anal. Appl., 238 (1999), 491-515. [MR: 2000k #46035], [ZBl: 941.46015] Hivatkozasok: H268. M. Muresan, Introducere in controlul optimal, Risoprint, Cluj-Napoca, 1999. H269. A. Petrusel | Gh. Mot, Convexity and decomposability in multivalued analysis, in Generalized Convexity and Generalized Monotonicity (Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, 1999) (eds. N. Hadjisavvas, J. E. Martnez-Legaz and J.-P. Penot), Lect. Notes in Econ. and Math. Systems, vol. 502, Springer Verlag, Berlin{Heidelberg, 2001, pp. 332340.
[87] Zs. Pales, Strong Holder and Minkowski inequalities for quasiarithmetic means, Acta Sci. Math. (Szeged), 65 (1999), 493-503. [MR: 2001d #26047], [ZBl: 980.26010] [88] K. Nikodem | Zs. Pales | Sz. Wasowicz, Abstract separation theorems of Rode type and their applications, Ann. Polonici Math. 72 (1999), 207-217. [MR: 2001c #26013], [ZBl: 956.39020] [89] Zs. Pales, Ujabb modszerek a fuggvenyegyenletek es a fuggvenyegyenl}otlensegek elmeleteben, akademiai doktori ertekezes, KLTE Debrecen, 1999. Hivatkozas:
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H270. A. Gilanyi, On approximately monomial functional, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 99-112.
[90] Zs. Pales, Nonconvex functions and separation by power means, Math. Inequal. Appl. 3 (2000), 169-176. [MR: 2000k #26011], [ZBl: 947.26010] Hivatkozas: H271. L. Losonczi, Conditional convexity, J. Math. Anal. Appl. 252 (2000), 1006-1017. [91] Gy. Maksa | A. A. J. Marley | Zs. Pales, On a functional equation arising from joint-receipt utility models, Aequationes Math. 59 (2000), 273-286. [MR: 2001h #39032], [ZBl: 962.39014] Hivatkozas: H272. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[92] P. Czinder | Zs. Pales, A general Minkowski-type inequality for two variable Gini means, Publ. Math. Debrecen, 57 (2000), 203-216. [MR: 2001i #26017], [ZBl: 963.26009] [93] K. Nikodem | Zs. Pales | Sz. Wasowicz, Multifunctions with selections of convex and concave type, Math. Pannonica 11 (2000), 249-292. [MR: 2001h #54036], [ZBl: 973.26011] [94] Z. Daroczy | Gy. Maksa | Zs. Pales, Extension theorems for the Matkowski-Sut^o problem, Demonstratio Math. 33 (2000), 547-556. [MR: 2002a #39027], [ZBl: 965.39018] Hivatkozasok: H273. Z. Daroczy | G. Hajdu | C. T. Ng, A Matkowski Sut^o problem for weighted quasi-arithmetic means, Acta Sci. Math. (Szeged), kozlesre elfogadva. H274. Z. Daroczy | G. Hajdu | C. T. Ng, An extension for a Matkowski Sut^o problem, Colloq. Math. 95 (2003), 153-161. H275. D. Glazowska | W. Jarczyk | J. Matkowski, Arithmetic mean as a linear combination of two quasiarithmetic means, Publ. Math. Debrecen, 61 (2002), 455-467. H276. G. Hajdu, An extension theorem for the Matkowski{Sut^o problem for conjugate arithmetic means, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 201-208. H277. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[95] Zs. Pales, Bernstein{Doetsch-type results for general functional inequalities, dedicated to Zenon Moszner's 70th birthday, Rocznik Nauk.-Dydakt. Prace Mat. 17 (2000), 197-206. [MR: 2001k #26015], Hivatkozasok: H278. M. Adamek, On -quasiconvex and -convex functions, Radovi Math. 11 (2002/03), 171-181. H279. M. Adamek, A characterization of -convex functions, kozlesre elfogadva. H280. K. Nikodem, Continuity properties of convex-type set-valued maps, J. Inequal. Pure Appl. Math., kozlesre elfogadva.
[96] Z. Boros | Zs. Pales | P. Volkmann, On stability for the Jensen equation on intervals, Aequationes Math. 60 (2000), 291-297. [MR: 2001m #39062], [ZBl: 986.39017] [97] Zs. Pales | V. Zeidan, Optimum problems with measurable set-valued constraints, SIAM J. Optim. 11 (2000), 426-443. [MR: 2002d #90115], [98] Z. Daroczy | Zs. Pales, On means that are both quasi-arithmetic and conjugate arithmetic, Acta Math. Hungar. 90 (2001), 271-282. [MR: 2003g #26034], [ZBl: 980.39014] Hivatkozasok: H281. Z. Daroczy, Matkowski-Sut^o type problem for conjugate arithmetic means, Rocznik Nauk.-Dydakt. Prace Mat. 17 (2000), 89-100. H282. Z. Daroczy | G. Hajdu | C. T. Ng, A Matkowski Sut^o problem for weighted quasi-arithmetic means, Acta Sci. Math. (Szeged), kozlesre elfogadva. H283. Z. Daroczy | G. Hajdu | C. T. Ng, An extension for a Matkowski Sut^o problem, Colloq. Math. 95 (2003), 153-161. H284. Z. Daroczy | Gy. Maksa, On a problem of Matkowski, Colloq. Math. 82 (1999), 117-123. H285. D. Glazowska | W. Jarczyk | J. Matkowski, Arithmetic mean as a linear combination of two quasiarithmetic means, Publ. Math. Debrecen, 61 (2002), 455-467. H286. G. Hajdu, An extension theorem for the Matkowski{Sut^o problem for conjugate arithmetic means, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 201-208. H287. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[99] J. Aczel | Gy. Maksa | Zs. Pales, Solution of a functional equation arising in an axiomatization of the utility of binary gambles, Proc. Amer. Math. Soc. 129 (2001), 483-493. [MR: 2001e #39008], [ZBl: 963.39026] Hivatkozasok:
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H288. J. Aczel | J-C. Falmagne | R. D. Luce, Functional equations in the behavioral sciences, Math. Japonica, 52(3) (2000), 469-512. H289. J. Aczel | R. D. Luce | C. T. Ng, Functional equations arising in a theory of rank dependence and homogeneous joint receipts, J. Math. Psychol. 47(2) (2003), 171-183. H290. R. D. Luce, Personal re ections on an unintentional behavioral scientist, Aequationes Math. 58 (1999), 3-15. H291. R. D. Luce, Utility of gains and losses: Measurement-theoretical and Experimental Approaches, Scienti c Psychology Series, Lawrence Erlbaum Associates, Publishers, Mahwah{New Jersey{London, 2000. H292. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[100] J. Aczel | Gy. Maksa | C. T. Ng | Zs. Pales, A functional equation arising from ranked additive and separable utility, Proc. Amer. Math. Soc. 129 (2001), 989-998. [MR: 2002c #39023], [ZBl: 967.39007] Hivatkozasok: H293. J. Aczel, A couple of functional equations applied to utility theory, Rocznik Nauk.-Dydakt. Prace Mat. 17 (2000), 9-20. H294. J. Aczel | J-C. Falmagne | R. D. Luce, Functional equations in the behavioral sciences, Math. Japonica, 52(3) (2000), 469-512. H295. J. Aczel | R. D. Luce | C. T. Ng, Functional equations arising in a theory of non-commutative joint receipt, kozlesre benyujtva. H296. J. Aczel | Gy. Maksa, A functional equation generated by event commutativity in separable and additive utility theory, Aequationes Math. 62 (2001), 160-174. H297. R. D. Luce, Personal re ections on an unintentional behavioral scientist, Aequationes Math. 58 (1999), 3-15. H298. R. D. Luce, Utility of gains and losses: Measurement-theoretical and Experimental Approaches, Scienti c Psychology Series, Lawrence Erlbaum Associates, Publishers, Mahwah{New Jersey{London, 2000. H299. R. D. Luce | A. A. J. Marley, Separable and additive representation of binary gambles of gains, Math. Social Sci. 40 (2000), 277-295. H300. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[101] L. Molnar | Zs. Pales, ? -order automorphisms of Hilbert space e ect algebras: the 2-dimensional case, J. Math. Physics 42 (2001), 1907-1912. [MR: 2001m #47141], Hivatkozasok: H301. P. Lahti | M. Maczynski | K. Ylinen, Unitary and antiunitary operators mapping vectors to parallel or to orthogonal ones, with applications to symmetry transformations, Letters in Math. Phys. 55 (2001), 43-51. H302. L. Molnar, Characterization of the automorphisms of Hilbert space e ect algebras, Commun. Math. Phys. 223 (2001), 437-450.
[102] Zs. Pales, Hyers-Ulam stability of the Cauchy functional equation on square-symmetric groupoids, Publ. Math. Debrecen, 58 (2001), 651-666. [MR: 2002f #39058], [ZBl: 980.39022] Hivatkozas: H303. K. Baron | P. Volkmann, On functions close to homomorphisms between square symmetric structures, http://www.mathematik.uni-karlsruhe.de/semlv, Seminar LV, 14 (2002), 12 pp.
[103] Zs. Pales, Separation theorems for convex sets and convex functions with invariance properties, in Generalized Convexity and Generalized Monotonicity (Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, 1999) (eds. N. Hadjisavvas, J. E. MartnezLegaz and J.-P. Penot), Lect. Notes in Econ. and Math. Systems, vol. 502, Springer Verlag, Berlin{ Heidelberg, 2001, pp. 279-293. [MR: 2002e #46005], [104] Z. Daroczy | Zs. Pales, On a class of means of several variables, Math. Inequal. Appl. 4 (2001), 331-341. [MR: 2002d #26027], [ZBl: 990.26018] [105] Gy. Maksa | Zs. Pales, Hyperstability of a class of linear functional equations, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 17 (2001), 107-112. [MR: 2003f #39090], [ZBl: 1004.39022] [106] Zs. Pales | V. Zeidan, The critical tangent cone in second-order conditions for optimal control, (Third World Congress of Nonlinear Analysts), Nonlinear Anal., Theory, Methods, Appl. 47 (2001), 1149-1161. [107] Zs. Pales, Separation by approximately convex functions, in Contributions to the Theory of Functional Equations II (eds. D. Gronau and L. Reich), Grazer Math. Ber. 344 (2001), 43-50. [MR: 2003f #26011], [108] A. Gilanyi | Zs. Pales, A regularity theorem for composite functional equations, Arch. Math. (Basel) 77 (2001), 317-322. [MR: 2002h #39031], [ZBl: 992.39021]
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[109] K. Nikodem | Zs. Pales, On approximately Jensen-convex and Wright-convex functions, C. R. Math. Rep. Acad. Sci. Canada 23 (2001), 141-147. [MR: 2003a #39037], Hivatkozas: H304. J. Mrowiec, On the stability of Wright-convex functions, Aequationes Math. 65 (2003), 158-164. modszerek a fuggvenyegyenletek regularitaselmeleteben, Kozgy}ulesi el}oadasok, 2000. [110] Zs. Pales, Uj majus, II. kotet, Magyar Tudomanyos Akademia, 2001, 415-432. [111] Zs. Pales, Az optimum els}o- es magasabb rend}u feltetelei, Kozgy}ulesi el}oadasok, 2000. majus, II. kotet, Magyar Tudomanyos Akademia, 2001, 565-574. [112] Z. Daroczy | Zs. Pales (Editors), Functional Equations | Results and Advances Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002. [MR: 2003b #39028], [ZBl: 983.00041] [113] Z. Daroczy | Zs. Pales, A Matkowski-Sut^o type problem for quasi-arithmetic means of order , Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 189-200. [MR: 2003e #39045], [114] K. Lajko | Zs. Pales, On a Mikusinski{Jensen functional equation, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 81-87. [MR: 2003e #39048], [115] Zs. Pales, Problems in the regularity theory of functional equations, Aequationes Math. 63 (2002), 1-17. [MR: 2003h #39017], Hivatkozas: H305. J. Matkowski, Solution of a regularity problem in equality of Cauchy means, Publ. Math. Debrecen, kozlesre elfogadva.
[116] Zs. Pales, Extension theorem for functional equations with bisymmetric operations, Aequationes Math. 63 (2002), 266-291. [MR: 2003f #39091], [ZBl: 1004.39021] Hivatkozasok: H306. K. Lajko, On a functional equation of Alsina and Garcia-Roig, Publ. Math. Debrecen 52 (1998), 517-515. H307. A. Gilanyi, On locally monomial functions, Publ. Math. Debrecen 51 (1997), 343-361.
H308. A. Gilanyi, Local stability and global superstability of monomial functional equations, Advances in Equations and Inequalities (ed. J. M. Rassias), Hadronic Press, Palm Harbor, 1999, 73-95. H309. A. Gilanyi, On approximately monomial functional, Functional Equations | Results and Advances (eds. Z. Daroczy | Zs. Pales), Kluwer Acad. Publ., Dordrecht, Advances in Math. Vol. 3, 2002, pp. 99-112. H310. Gy. Maksa, Ujabb eredmenyek a fuggvenyegyenletek elmeleteben, Habilitacios ertekezes, Debreceni Egyetem, Debrecen, 2000.
[117] Z. Daroczy | Zs. Pales, Gauss composition of means and the solution of the Matkowski-Sut^o problem, Publ. Math. Debrecen, 61 (2002), 157-218. [MR: 2003x #], [ZBl: p 1006.39020] Hivatkozasok: H311. Z. Daroczy, Gaussian iteration of mean values and the existence of 2, Teaching of Math. Comp. Sci. 1 (2003), 35-42. H312. Z. Daroczy | G. Hajdu | C. T. Ng, A Matkowski Sut^o problem for weighted quasi-arithmetic means, Acta Sci. Math. (Szeged), kozlesre elfogadva. H313. Z. Daroczy | G. Hajdu | C. T. Ng, An extension for a Matkowski Sut^o problem, Colloq. Math. 95 (2003), 153-161.
[118] A. Gilanyi | Zs. Pales, On Dinghas-type derivatives and convex functions of higher-order, Real Anal. Exchange, 27 (2001/2002), 485-493. [MR: 2003f #26010], [119] G. Kassay | J. Kolumban | Zs. Pales, Factorization of Minty and Stampacchia variational inequality systems, European J. Oper. Res., 143 (2002), 377-389. [MR: 2003i #49012], Hivatkozas: H314. Y.-P. Fang | N.-J. Huang, Existence results for system of strong implicit vector variational inequalities, Acta Math. Hungar., kozlesre benyujtva.
[120] M. Bessenyei | Zs. Pales, Higher-order generalizations of Hadamard's inequality, Publ. Math. Debrecen, 61 (2002), 623-643. [121] Zs. Pales | V. Zeidan, Strong local optimality conditions for control problems with mixed statecontrol constraints, Proceedings of the 41st IEEE Conference on Decision and Control, 2002, pp. 4738-4743. [122] Zs. Pales, On approximately convex functions, Proc. Amer. Math. Soc. 131 (2003), 243-252. [MR: 2003h #26015], [123] E. Neuman | Zs. Pales, On comparison of Stolarsky and Gini means, J. Math. Anal. Appl. 278 (2003), 274-285. Hivatkozas: H315. E. Neuman | J. Sandor, Inequalities involving Stolarski and Gini means, Math. Pannon. 14 (2003), 29-44.
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[124] R. Badora | R. Ger | Zs. Pales, Additive selections and the stability of the Cauchy functional equation, ANZIAM J. 44 (2003), 323-337. Hivatkozas: H316. L. Szekelyhidi, Ulam's problem, Hyers's solution | and to where they led, Functional Equations and Inequalities, (ed. Th. M. Rassias), Mathematics and Its Applications, Vol. 518, Kluwer Acad. Publ., Dordrecht{Boston{London, 2000, pp. 259-285.
[125] Z. Daroczy | Zs. Pales, On functional equations involving means, Publ. Math. Debrecen, 62 (2003), 363-377. [126] P. Czinder | Zs. Pales, Minkowski-type inequalities for two variable Stolarsky means, Acta Sci. Math. (Szeged) 69 (2003), 27-47. Hivatkozas: H317. L. Losonczi, Inequalities for Cauchy mean values, Math. Inequal. Appl. 5 (2002), 349-359. [127] M. Adamek | K. Nikodem | Zs. Pales, On (K; )-convex set-valued maps, Radovi Mat. 11 (2002/03), 183-191. Hivatkozas: H318. K. Nikodem, Continuity properties of convex-type set-valued maps, J. Inequal. Pure Appl. Math., kozlesre elfogadva.
[128] Z. Daroczy | Zs. Pales, The Matkowski-Sut^o type problem for weighted quasi-arithmetic means, Acta Math. Hungar. 100 (2003), 237-243. Hivatkozas: H319. Z. Daroczy | G. Hajdu | C. T. Ng, An extension for a Matkowski Sut^o problem, Colloq. Math. 95 (2003), 153-161.
[129] M. Bessenyei | Zs. Pales, Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl. 6 (2003), 379-392.
Megjelenes alatt allo es kozlesre elfogadott dolgozatok [130] Zs. Pales, A regularity theorem for composite functional equations, Acta Sci. Math. (Szeged). [131] A. Gilanyi | K. Nikodem | Zs. Pales, Bernstein-Doetsch type results for quasiconvex functions, Math. Inequal. Appl. Hivatkozas: H320. M. Adamek, On -quasiconvex and -convex functions, Radovi Math. 11 (2002/03), 171-181. [132] Z. Daroczy | Gy. Maksa | Zs. Pales, On two variable means weighted by weight functions, Aequationes Math. [133] A. Hazy | Zs. Pales, On approximately midconvex functions, Bull. London Math. Soc. [134] Zs. Pales | V. Zeidan, Optimal control problems with set-valued control and state constraints, SIAM J. Optim. [135] Zs. Pales | V. Zeidan, Strong local optimality conditions for state constrained control problems, J. Global Optim. [136] K. Nikodem | Zs. Pales, On t-convex functions, Real Anal. Exchange. Hivatkozas: H321. M. Adamek, A characterization of -convex functions, kozlesre elfogadva.
[137] Z. Daroczy | Zs. Pales, A Matkowski{Sut^o-type problem for weighted quasi-arithmetic means, Annales Univ. Sci. Budapest, Sect. Comp. [138] Z. Daroczy | Zs. Pales, Kozepertekek Gauss-fele kompozcioja es a Matkowski-Sut^o problema megoldasa, Mat. Lapok. [139] Zs. Pales | V. Zeidan, Critical and critical tangent cones in optimization problems, J. Set-Valued Anal. [140] Zs. Pales | L. Szekelyhidi, On approximate sandwich and decomposition theorems, Annales Univ. Sci. Budapest, Sect. Comp.
Egyetemi jegyzetek [141] Zs. Pales, Felteteles szels}oertekszamtas, egyetemi jegyzet, KLTE Debrecen, 1989. [142] Zs. Pales, Bevezetes az analzisbe, egyetemi jegyzet, KLTE Debrecen, 1998.
Osszes tes:
Szerkesztett konyv, konferenciakotet: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Referalt folyoiratokban es konferenciakiadvanyokban megjelent dolgozatok: . . . . . . . . . . . . . . . . . . . . . . . . . 123 Kozlesre elfogadott dolgozatok: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Disszertaciok, tezisek: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Egyetemi jegyzet: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Osszes ismert hivatkozasok szama: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
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